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Theorem 3orcomb 929
Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)
Assertion
Ref Expression
3orcomb  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )

Proof of Theorem 3orcomb
StepHypRef Expression
1 orcom 680 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
21orbi2i 712 . 2  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ch  \/  ps ) ) )
3 3orass 923 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
4 3orass 923 . 2  |-  ( (
ph  \/  ch  \/  ps )  <->  ( ph  \/  ( ch  \/  ps ) ) )
52, 3, 43bitr4i 210 1  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ch  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662    \/ w3o 919
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115  df-3or 921
This theorem is referenced by:  eueq3dc  2767  sotritrieq  4088
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